Title:Noise corrections to stochastic trace formulas

Abstract: We review studies of an evolution operator L for a discrete Langevin equation
with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading
eigenvalue of L yields a physically measurable property of the dynamical
system, the escape rate from the repeller. The spectrum of the evolution
operator L in the weak noise limit can be computed in several ways. A method
using a local matrix representation of the operator allows to push the
corrections to the escape rate up to order eight in the noise expansion
parameter. These corrections then appear to form a divergent series. Actually,
via a cumulant expansion, they relate to analogous divergent series for other
quantities, the traces of the evolution operators L^n. Using an integral
representation of the evolution operator L, we then investigate the high order
corrections to the latter traces. Their asymptotic behavior is found to be
controlled by sub-dominant saddle points previously neglected in the
perturbative expansion, and to be ultimately described by a kind of trace
formula.